What is ln(9^{3x-2})+ln(9^{3x-3}) ?

The solution to ln(9^{3x-2})+ln(9^{3x-3}) is 2ln(3)(6x-5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(9^{3x-2})+ln(9^{3x-3})

simplify

ln (9^{3 x - 2}) + ln (9^{3 x - 3})

2 ln (3) (6 x - 5)

Solution steps

ln (9^{3 x - 2}) + ln (9^{3 x - 3})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (9^{3 x - 2}) + ln (9^{3 x - 3}) = ln (9^{3 x - 2} \cdot 9^{3 x - 3})

= ln (9^{3 x - 2} \cdot 9^{3 x - 3})

Simplify

9^{3 x - 2} \cdot 9^{3 x - 3} : 9^{6 x - 5}

= ln (9^{6 x - 5})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= ln (9) (6 x - 5)

Simplify

ln (9) : 2 ln (3)

= 2 ln (3) (6 x - 5)

ln (- 2) + ln (- 3)

lo g_{10} (t^{x} (1 - t)^{1 - x})

0.48 - \frac{0.0592}{6} lo g_{10} (\frac{1.5}{0.5})

ln (\frac{19}{44})

What is ln(9^{3x-2})+ln(9^{3x-3}) ?
The solution to ln(9^{3x-2})+ln(9^{3x-3}) is 2ln(3)(6x-5)